Brandon is 20 years younger than Kevin. Nineteen years ago, Kevin was 3 times older than Brandon. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Brandon. Let Kevin's current age be $k$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $k = b + 20$ Nineteen years ago, Kevin was $k - 19$ years old, and Brandon was $b - 19$ years old. The information in the second sentence can be expressed in the following equation: $k - 19 = 3(b - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = k - 20$ . Substituting this into our second equation, we get the equation: $k - 19 = 3($ $(k - 20)$ $ -$ $ 19)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 19 = 3k - 117$ Solving for $k$ , we get: $2 k = 98$ $k = 49$.